Multiangle static and dynamic light scattering in the intermediate scattering angle range E. Tamborini1,2, a) and L. Cipelletti1,2 1)Universit´eMontpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France 2)CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France (Dated: 21 May 2018) We describe a light scattering apparatus based on a novel optical scheme covering the scattering angle range 0.5 deg ≤ θ ≤ 25 deg, an intermediate regime at the frontier between wide angle and small angle setups that is difficult to access by existing instruments. Our apparatus uses standard, readily available optomechanical components. Thanks to the use of a charge-coupled device detector, both static and dynamic light scatter- ing can be performed simultaneously at several scattering angles. We demonstrate the capabilities of our apparatus by measuring the scattering profile of a variety of samples and the Brownian dynamics of a dilute colloidal suspension. PACS numbers: 07.60.-j,42.15.Eq, 42.30.Kq Keywords: static light scattering, dynamic light scattering, CCD I. INTRODUCTION dynamic). Wide-angle light scattering (WALS) setups often provide both SLS and DLS measurements, cov- Light scattering methods are a powerful tool for in- ering approximately the range 10 deg ≤ θ < 180 deg, −1 vestigating the structure and the dynamics of soft and corresponding to length scales of order 2πq ranging −1 biological matter. The typical space and time scales that from 0.2 µm to 2.3 µm. Here q = 4πnλ sin(θ/2) is are probed range from tens of nanometers to tens of mi- the scattering vector, with n the solvent refractive in- crons, and from a fraction of a microsecond to several dex, λ the in-vacuo laser wavelength and θ the scatter- hours, respectively. Typical applications include particle ing angle. However, it should be noted that in practice sizing, the characterization of aggregation phenomena, it is difficult to obtain reliable data below θ = 20 deg, the determination of interparticle interactions, the inves- because the cylindrical sample geometry that it is usu- tigation of the structure and the relaxation dynamics of ally adopted in WALS limits the quality of the optical complex fluids. The diversity of systems that can be interfaces. Small-angle and ultra-small-angle light scat- studied makes the technique appealing for both academic tering setups (SALS and USALS, respectively) are spe- laboratories and industry: suspensions of colloidal par- cialized for measurements close to the forward direction, ticles or emulsions, solutions of polymers and proteins, with scattering angles covering up to two decades, up to foams, and surfactant phases are but a few examples of approximately 10 deg for SALS and a few degrees for such systems. USALS. The corresponding length scales vary between a Scattering methods may be divided in two classes: few microns and tens or even hundreds of microns. While static and dynamic light scattering. In static light scat- some of these setups use dedicated photodiode detectors 3–6 tering (SLS)1, one probes the structure of a sample optimized for SLS but unfit for DLS , the adoption of by measuring the time-averaged scattered intensity as a CCD or CMOS detector is increasingly popular, since a function of the scattering angle. By contrast, dy- it allows for both static and dynamic light scattering to 7,8 namic light scattering (DLS)2 focuses on the temporal be performed , as first shown by the pioneering work of 7 fluctuations of the scattered intensity in order to extract Wong and Wiltzius . valuable information on the sample dynamics. In both arXiv:1208.6393v1 [physics.optics] 31 Aug 2012 It should be noted that there is little if any overlap cases, the sample is typically illuminated by a laser beam, between the range of scattering angles of typical WALS while photodiodes, avalanche photodiodes, photomulti- and SALS or USALS setups: this leaves uncovered a cru- plier tubes or CCD or CMOS cameras are used as a de- cial angular range corresponding to probed length scales tector. on the order of a micron, the characteristic size of many A wide variety of light scattering apparatuses have colloidal objects of industrial and fundamental science been developed, many of which are commercially avail- interest. Additionally, absolute intensity measurements able. The design of a setup is in general optimized ac- are notoriously difficult in light scattering, especially for cording to the range of scattering angles to be covered SALS or USALS, thus making it difficult to merge data and the kind of measurements to be performed (static or from different setups on the same scale. To circumvent this problem, a few apparatuses covering the “mid an- gle” range (mid-angle light ccattering, MALS) have been proposed in the past. The apparatus described in Ref.4 a)Electronic mail: [email protected] covers an impressive angular range (2deg −60 deg), using 2 a custom made cell and dedicated photodiode arrays and layouts in Sec. II. We then present our new MALS appa- electronics. Ferri and coworkers report a setup covering ratus in Sec. III, before describing its angular calibration scattering angles up to 15deg5,6, using a commercially in Sec.V. A series of tests of the apparatus’ performances available cell but again a custom photodiode array with for both SLS and DLS are presented in Sec. VI, before dedicated electronics. A different approach is used in the the concluding remarks of Sec. VII. commercially available apparatus of Ref.9, which covers scattering angles from a fraction of degree up to about 40 deg by varying the propagation direction of the inci- dent beam. Accordingly, several distinct measurements are required to sample the full angular range, each mea- surement covering about 5 deg. Chou and Hong10 report a CCD-based setup in the range 2deg <θ< 25 deg using II. POPULAR OPTICAL LAYOUTS FOR SALS AND a scheme originally proposed by Ferri for SALS3. Unfor- USALS tunately, however, no detailed description and charac- terization of the apparatus performances are provided. Finally, one may take advantage of the good-quality op- Most MALS setups are based on the same optical lay- out as that for SALS and USALS, examples of which are tics of modern microscopes to build an apparatus that combines imaging with low- or mid-angle scattering. Ka- shown in Fig. 1. In the top scheme, Fig. 1a, adopted in Refs.4,9,14,15, the scattered intensity is measured in the plan et al.11 report a DLS apparatus based on an in- focal plane Σ of a so-called Fourier lens of focal length verted microscope that covers scattering angles between 20.6deg and 55.1 deg, while Celli et al.12 demonstrate f. Neglecting refractions at the solvent-cell and cell-air interfaces, a point on Σ at a distance r from the optical DLS in a upright microscope for θ ≤ 12 deg. In both −1 cases, measurements are performed at one single angle axis corresponds to a scattering angle θ = arctan(rf ). In order to avoid artifacts due to light leaking from at a time. In Ref.13, a microscope- and CCD-based static light scattering instrument is presented, covering the intense transmitted beam, a hole may be drilled in the detector to let the transmitted beam pass through the range 0.9 µm ≤ q ≤ 18 µm, corresponding approxi- 4–6,14,15 mately to 3.3deg ≤ θ ≤ 70 deg. Σ . Alternatively, a screen may be placed in the plane Σ and a CCD camera may be used to record the 10,13 With the exception of the setups of Refs. that intensity distribution on the screen. In both cases, this could in principle be extended to DLS, these appara- geometry prevents a CCD camera to be placed directly tuses are unfit for simultaneous static and dynamic light in the plane Σ, making DLS measurements impossible. scattering at multiple angles, either because the angu- In addition, detectors and lenses used in this configu- 9,11,12 lar range is sampled sequentially, as in Refs. , or ration must often be custom-made to efficiently remove because photodiodes that cover a very large number of the transmitted beam and to limit aberrations associated 4–6 speckles are used, as in Refs. , a design not appropri- with large scattering angles. The scheme of Fig. 1b, de- 2 ate for DLS . It is worth noting that photodiode ar- scribed in Refs.5,6, is equivalent to the top one, provided rays are typically larger than CCD or CMOS detectors: that one replaces f by the sample-detector distance dΣ in this makes it difficult to transpose the optical layout of the calculation of θ16. The advantage is that large scat- Refs.4–6 to a CCD-based apparatus and would impose tering angles may be attained simply by reducing dΣ, extra constraints on the cell dimensions, in particular its without changing f and with no stringent requirements thickness L, as we shall discuss it in the following. Ad- on the numerical aperture of the Fourier lens. However, ditionally, photodiode arrays can easily accommodate a the sample thickness L must satisfy L <<dΣ, since the small hole to let through the transmitted beam, a crucial mapping between r and θ depends on the distance of a requirement for small angle measurements, while this is scatterer from Σ. When using a CCD detector, typical not possible for a CCD or CMOS detector. Thus, exist- values of dΣ are a few cm at most, limiting L to about ing designs for MALS cannot be easily generalized to an 1 mm. Additionally, the remarks on removing the trans- apparatus for both SLS and DLS.